While macOS is a very robust operating system, sometimes there can be hiccups when performing system updates. In my case, the progress bar stopped and stayed that way for a few hours.
If you are experiencing a frozen Mac when updating the system, here are a few ways to save your data, attack the problem, and solve the issue.

A very quick and easy thing to do that could save you a lot of hassle with stuck updates (or other malfunctioning Apple services) is to go to the official Systems Status page. Here you’ll see the status of just about every Apple service you can think of. Look over at the status of “macOS Software Update” to see whether the update servers are working as they should. If the bubble is green, then they’re fine and the issue lies elsewhere. If it’s red or yellow, then you’re just going to have to sit out the problem until servers are back to normal.

Speaking of sitting it out

Conclusion

Hopefully these steps were able to get you back on track. If not, you are advised to contact Apple Support for a further look.

As stated, these hiccups rarely do happen, but when they do it is nice to know that macOS includes features capable of working them out.